SCERT Maharashtra solutions for Algebra (Mathematics 1) [English] 10 Standard SSC chapter 1 - Linear Equations in Two Variables [Latest edition]

To draw the graph of 4x + 5y = 19, if x = 1 is taken then what will be the value of y?

For the equations with variables x and y, if Dx = 26, Dy = −39 and D = 13 then x = ?

Which of the following is linear equation in two variables?

Which of the following is not the solution of 3x + 6y = 12?

`|(3, 5),(2, x)|` = 2 ∴ x = ______

For equations 5x + 3y + 11 = 0 and 2x + 4y = −10 find D.

If 49x – 57y = 172 and 57x – 49y = 252 then x + y = ?

The solution of the equation 2x – y = 2 is ______

The solution of the equation x − y = 10 and x + y = 70 is ______

Find the value of D_x for the equation 4x + 3y = 19 and 4x − 3y = −11

State with reason whether the equation 3x² − 7y = 13 is a linear equation with two variables?

Show the condition using variables x and y: Two numbers differ by 3

For the equation 4x + 5y = 20 find y when x = 0

Write any two solutions of the equation x + y = 7

Decide whether (0, 2) is the solution of the equation 5x + 3y = 6

Write any two solutions of the equation a – b = – 3

If x + 2y = 5 and 2x + y = 7, then find the value of x + y

If Dx = 24 and x = – 3, then find the value of D

The cost of the book is 5 rupees more than twice the cost of a pen. Show this using linear equation by taking cost of book(x) and cost of a pen(y)

If `"a"/4 + "b"/3` = 4, write the equation in standard form

Complete the table to draw the graph of 2x – 3y = 3,

Solve the following to find the value of following determinant.

`|(3, -2),(4, 5)| = 3 xx square - square xx 4 = square + 8 = square`

Complete the activity to find the value of x.
3x + 2y = 11 …(i) and 2x + 3y = 4 …(ii)
Solution:
Multiply equation (i) by _______ and equation (ii) by _______.
`square` × (3x + 2y = 11)    ∴ 9x + 6y = 33 …(iii)
`square` × (2x + 3y = 4)      ∴ 4x + 6y = 8   …(iv)
Subtract (iv) from (iii),
`square` x = 25
∴ x = `square`

If (2, 0) is the solution of 2x + 3y = k then finds the value of k by completing the activity

Solution: (2, 0) is solution of the equation 2x + 3y = k

Putting x = `square` and y = `square`

∴ `2(square) + 3 xx 0` = k

∴ 4 + 0 = k

∴ k = `square`

To find the values of x and y for the equations x − 2y = 5 and 2x + 3y = 10 complete the activity.

D = `|(1, -2),(2, 3)|` = 3 + 4 = 7

D_x = `|(5, -2),(10, 3)| = square`

D_y = `|(1, 5),(2, 10)| = square`

By Cramer’s rule

x = `("D"_x)/"D" = square,` y = `("D"_y)/"D" = square`

The difference between an angle and its complement is 10° find measure of the larger angle.

Find the value of `|(5, 2),(0, -1)|`

For the equations y + 2x = 19 and 2x – 3y = − 3, find the value of D.

In the equation 2x – y = 2 if x = 3, then find y = ?

If (2, −5) is the solution of the equation 2x − ky = 14, then find k = ?

For the equation a + 2b = 7, find a when b = 4

Decide whether x = 2 and y = − 1 is the solution of the equation 2x + y = 3 or not?

Using variables a and b write any two equations whose solution is (0, 2).

If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?

State with reason whether the point (3, −2) will lie on the graph of the equation 5m – 3n = − 21

Complete the activity.

Complete the following table to draw the graph of 3x − 2y = 18

The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.

Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.

∴ The number = 10x + y

∴ The number obtained by interchanging the digits = `square`

∴ The sum of the number and the number obtained by interchanging the digits = 132

∴ 10x + y + 10y + x = `square`

∴ x + y = `square`      .....(i)

By second condition,

Digit in the ten’s place = digit in the unit’s place + 2

∴ x – y = 2     ......(ii)

Solving equations (i) and (ii)

∴ x = `square`, y = `square`

Ans: The original number = `square`

Solve the given simultaneous equations graphically x + y = 5 and y = 5

Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay

Solve by Cramer’s rule, 3x – 4y = 10, 4x + 3y = 5

Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers

Solve: 4m – 2n = – 4, 4m + 3n = 16

Solve: 99x + 101y = 499, 101x + 99y = 501

The length of the rectangle is 5 more than twice its breadth. The perimeter of a rectangle is 52 cm, then find the length of the rectangle

The graph of the equations 2x − y − 4 = 0 and x + y + 1 = 0 intersect each other in point P(a, b), then find the coordinates of P?

The solution of the equation ax + by + 5 = 0 and bx − ay − 12 = 0 is (2, – 3). Find the values of a and b

A person starts a job with a fixed salary and yearly increment. After 4 years his salary is ₹ 15000 and after 10 years it becomes ₹ 18000. Then find his monthly salary and increment

For the equation 3x − 2𝑦 = 17, find the value of x when y = −1 and find the value of y when x = 3

Solve the following equations by graphical method, x − y = 1, 2x + y = 8

Using the determinants given below form two linear equations and solve them.

D = `|(5, 7),(2, -3)|`, Dy = `|(5, 4),(2, -10)|`

For an A.P., t₁₇ = 54 and t₉ = 30 find the first term(a) and common difference(d)

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train was slower by 6 km/h it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Solve 0.4x + 0.3y = 1.7; 0.7 x − 0.2y = 0.8

The semi perimeter of a rectangular shape garden is 36 m. The length of the garden is 4 m more than its breadth. Find the length and the breadth of the garden

Form the simultaneous linear equations using the determinants

D = `|(4, -3),(2, 5)|`, D_x = `|(5, -3),(9, 5)|`, D_y = `|(4, 5),(2, 9)|`

I held a number 75 in my mind. Write any condition showing the relation between their digits. Write the condition showing the relation between the number and the number obtained by interchanging the digits

Write any two linear equations in two variables in which the value of one variable is 12 and the other 10

From the railway station I took a rickshaw to go home. It is decided that I have to pay ₹ X for the first kilometre and for each kilometre ₹ Y for the next. For 10 kilometres the fare is ₹ 40 and for 16 kilometres fare is ₹ 58. Find the fare for the first kilometre